The European Union is set to throw embattled British Prime Minister Theresa May a lifeline in Brexit talks because of concern that the biggest risk to getting a deal done is now whether she can cling to power.

EU officials say negotiators won't reject outright the U.K.'s blueprint for how to leave the organization despite opposing several major elements of it. May's plan to keep the U.K. closely tied to the EU's single market after Brexit, the core of her policy paper published on Thursday, will kick start talks that had hit a brick wall after more than a year of back and forth.

The stance highlights how precarious May's position has become. A week that started with a rare show of unity on Brexit by her government then led to two senior ministers quitting within 24 hours of each other and rebels within her own party dismissing her plan as a betrayal of what voters decided in the 2016 referendum.